Modeling from a trader's perspective

I was trading professionally in the years 2006-2014 in the equity derivatives market. This thesis deals with two of the ideas inspired by my experience as a professional trader. The first topic deals with the pricing of a derivatives product in the market with a specific risk concentration. We call the product that causes the concentration a market driver. When the market driver exists, not only the market driver itself, but any derivatives product will not be priced fairly. We introduced a new model based on the Heston model that accounts for the concentration. The model leads to a pair of partial differential equations (PDEs): one semilinear parabolic PDE to price the market driver and one linear parabolic PDE to price all the other products. In solving the semilinear PDE, we use the policy improvement algorithm (PIA) to approximate the solution with those of linear PDEs. We show that the approximated solutions satisfy quadratic local convergence (QLC) which explains the efficiency of the algorithm. This efficiency of the algorithm is proved in a more general setup. The other idea sparked by my experience that is explored in the last chapter of the thesis concerns modeling technical analysis. Technical analysis is a family of methods that traders use to make decisions to purchase/sell assets. There is no mathematical proof that shows that they are correct as far as I am aware. We focus on one of the methods, the method of support and resistance levels, and used the optimal stopping argument to show the validity of the method. As far as I know, this is one of the first results to mathematically prove the effectiveness of a method in technical analysis

INVESTIGATION OF A THEORETICAL MODEL FOR THE ROTATIONAL SHOT PUT TECHNIQUE

This study aimed to investigate the causal relationships among biomechanical variables for achieving high release velocity in male shot putter and create a theoretical model for the rotational shot put technique. The throwing motions of 22 male shot putters were videotaped and analysed using the 3D DLT method. Path analysis was used to examine causal relationships among biomechanical variables. The examined model consisted of three kinetic and eight kinematic variables that significantly related to a higher release velocity directly or indirectly. Two key factors were identified in shot put performance with the rotational technique: (1) increasing of impulse of the shot at delivery phase, and (2) creating greater linear and angular momentum before delivery. Future research should confirm or extend this potential causal mechanism of contributors to shot release velocity

The final fate of instability of Reissner-Nordstr\"om-anti-de Sitter black holes by charged complex scalar fields

We investigate instability of 4-dimensional Reissner-Nordstr\"om-anti-de Sitter (RN-AdS$_4$) black holes with various topologies by charged scalar field perturbations. We numerically find that the RN-AdS$_4$ black holes become unstable against the linear perturbations below a critical temperature. It is analytically shown that charge extraction from the black holes occurs during the unstable evolution. To explore the end state of the instability, we perturbatively construct static black hole solutions with the scalar hair near the critical temperature. It is numerically found that the entropy of the hairly black hole is always larger than the one of the unstable RN-AdS$_4$ black hole in the microcanonical ensemble. Our results support the speculation that the black hole with charged scalar hair always appears as the final fate of the instability of the RN-AdS$_4$ black hole.Comment: 9 pages, 4 figures. To appear in PR

Meissner effect in the layered Kane-Mele model with Hubbard interaction

We investigate the magnetic response in the quantum spin Hall phase of the layered Kane-Mele model with Hubbard interaction, and argue a condition to obtain the Meissner effect. The effect of Rashba spin orbit coupling is also discussed.Comment: 4 pages, accepted for publication in Journal of Physics: Conference Series as proceedings of International Symposium "Nanoscience and Quantum Physics 2011" (nanoPHYS'11) held in Toky